International Journal of Scientific Engineering and Technology

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Orthogonal Hybrid Functions (HF) for Solving Second Order Differential Equations Using One-Shot Integration Operational Matrices


Affiliations
1 Department of Electrical Engineering, St. Thomas’ College of Engineering and Technology, Kolkata, India
2 Department of Applied Physics, Calcutta University, Kolkata, India
 

The present work employs a new set of orthogonal hybrid functions (HF) generated from the synthesis of orthogonal sample-and-hold functions (SHF) and triangular functions (TF).

The one-shot operational matrices for second order integration are derived. These matrices are employed for more accurate second order integration. Finally, these matrices are employed for solving second order non-homogeneous differential equations followed by a numerical example. The results are compared with the exact solution as well as the results obtained via 4th order Runge-Kutta method.


Keywords

Hybrid Functions, Sample-And-Hold Functions, Triangular Functions, Function Approximation, Operational Matrices, Differential Equation.
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  • Orthogonal Hybrid Functions (HF) for Solving Second Order Differential Equations Using One-Shot Integration Operational Matrices

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Authors

A. Ganguly
Department of Electrical Engineering, St. Thomas’ College of Engineering and Technology, Kolkata, India
A. Deb
Department of Applied Physics, Calcutta University, Kolkata, India
G. Sarkar
Department of Applied Physics, Calcutta University, Kolkata, India

Abstract


The present work employs a new set of orthogonal hybrid functions (HF) generated from the synthesis of orthogonal sample-and-hold functions (SHF) and triangular functions (TF).

The one-shot operational matrices for second order integration are derived. These matrices are employed for more accurate second order integration. Finally, these matrices are employed for solving second order non-homogeneous differential equations followed by a numerical example. The results are compared with the exact solution as well as the results obtained via 4th order Runge-Kutta method.


Keywords


Hybrid Functions, Sample-And-Hold Functions, Triangular Functions, Function Approximation, Operational Matrices, Differential Equation.